Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #677 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4050 |
| Fitting | C2×C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ #135 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #13099290, #13099291, #13099293, … |
| maximal normal subgroup of | #13099290, #13099291, #13099293, … |
| maximal quotient of | C5×#64972, C4×C5×#677, C4×C5×D40, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 797);